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Van der Waerden number

Index Van der Waerden number

Van der Waerden's theorem states that for any positive integers r and k there exists a positive integer N such that if the integers are colored, each with one of r different colors, then there are at least k integers in arithmetic progression all of the same color. [1]

16 relations: Arithmetic progression, Electronic Journal of Combinatorics, Elwyn Berlekamp, Experimental Mathematics (journal), Geometric and Functional Analysis, Graph coloring, Grzegorczyk hierarchy, Journal of the American Mathematical Society, Mathematics of Computation, Natural number, Prime number, Primitive recursive function, Ramsey's theorem, Saharon Shelah, Timothy Gowers, Van der Waerden's theorem.

Arithmetic progression

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

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Electronic Journal of Combinatorics

The Electronic Journal of Combinatorics is a peer-reviewed open access scientific journal covering research in combinatorial mathematics.

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Elwyn Berlekamp

Elwyn Ralph Berlekamp (born September 6, 1940) is an American mathematician.

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Experimental Mathematics (journal)

Experimental Mathematics is a quarterly scientific journal of mathematics published by A K Peters, Ltd. until 2004, now by Taylor & Francis.

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Geometric and Functional Analysis

Geometric and Functional Analysis (GAFA) is a mathematical journal published by Birkhäuser, an independent division of Springer-Verlag.

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Graph coloring

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.

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Grzegorczyk hierarchy

The Grzegorczyk hierarchy (pronounced), named after the Polish logician Andrzej Grzegorczyk, is a hierarchy of functions used in computability theory (Wagner and Wechsung 1986:43).

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Journal of the American Mathematical Society

The Journal of the American Mathematical Society (JAMS), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society.

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Mathematics of Computation

Mathematics of Computation is a bimonthly mathematics journal focused on computational mathematics.

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Primitive recursive function

In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive).

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Ramsey's theorem

In combinatorial mathematics, Ramsey's theorem states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph.

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Saharon Shelah

Saharon Shelah (שהרן שלח) is an Israeli mathematician.

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Timothy Gowers

Sir William Timothy Gowers, (born 20 November 1963) is a British mathematician.

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Van der Waerden's theorem

Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory.

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References

[1] https://en.wikipedia.org/wiki/Van_der_Waerden_number

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